Adding and Subtracting Functions
Procedure —
To Evaluate the Sum or Difference of Functions
Step 1 Use x = a to find f(a) and g(a)
Step 2 Find f(a) + g(a) or f(a) - g(a).
Example 1
Given f(x) = x3 - 9 and g(x) = x2 + 18, find (f + g)(x) when x
= -2.
That is, find (f + g)(-2).
Solution
| Step 1 |
Use x = -2 to find f(-2) and g(-2). Substitute
-2 for x in f(x).
Simplify.
Subtract.
So, f(-2) = -17.
Substitute -2 for x in g(x).
Simplify.
Add.
So, g(-2) = 22.
|
f(-2)
g(-2) |
= (-2)3 - 9 = -8 - 9
= -17 = (-2)2 + 18 = 4 + 18 = 22 |
| Step 2 |
Find f(-2) = g(-2).
Add. |
f(-2) + g(-2) |
= -17 + 22 = 5 |
So, (f + g)(-2) = 5.
Example 2
Given f(x) = x4 + 20 and g(x) = 5x2, find (f - g)(x) when x
= 3.
That is, find (f - g)(3).
Solution
| Step 1 |
Use x = 3 to find f(3) and g(3). Substitute 3 for x in f(x).
Simplify.
So, f(3) = 101.
Substitute 3 for x in g(x).
Simplify.
So, g(3) = 45. |
f(3)
g(3) |
= (3)4 + 20
= 101 = 5(3)2 = 45 |
| Step 2 |
Find f(3) - g(3).
Subtract. |
f(3) - g(3) |
= 101 - 45
= 56 |
So, (f - g)(3) = 56.
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